`Lim_(x to 0 )( 2cosx-2+bx^2)/x^4`

If lim_(xto0) (f(x))/(sin^(2)x)=8,lim_(xto0) (g(x))/(2cosx-xe^(x)+x^(3)+x-2)=lamda" and " lim_(xto0) (1+2f(x))^((1)/(g(x)))=(1)/(e)," then" The value of lamda is

Let alpha and beta be the distinct root of ax^(2) + bx + c=0 then lim_(x to 0) (1- cos (ax^(2)+ bx+c))/((x-alpha)^(2)) is equal to

The value of lim_(xto0)(x cosx-log(1+x))/(x^(2)) is

lim_(x rarr 0) (2(1-cosx))/x^2

lim_(x to 0) ((1-cos 2x)(3+cosx))/(x tan 4x) is equal to

lim_(xto0) ((cos x)^(1//2)-(cosx)^(1//3))/(sin^2x) is

lim_ (x rarr0) (cos ax-cos bx) / (x ^ (2))

Evaluate lim_(x to 0) ("sin"^(2) 4x)/(x^(2))

The integer n for which the lim_(x to 0)(cos^(2)x-cosx-e^(x)cosx+e^(x)-(x^(3))/2)/(x^(n)) is a finite non-zero number is